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An Efficient Algorithm for 2D Euclidean 2-Center with Outliers

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Algorithms - ESA 2008 (ESA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5193))

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Abstract

For a set P of n points in ℝ2, the Euclidean 2-center problem computes a pair of congruent disks of the minimal radius that cover P. We extend this to the (2,k)-center problem where we compute the minimal radius pair of congruent disks to cover n − k points of P. We present a randomized algorithm with O(n k 7 log3 n) expected running time for the (2,k)-center problem. We also study the (p,k)-center problem in ℝ2 under the ℓ ∞ -metric. We give solutions for p = 4 in O(k O(1) n logn) time and for p = 5 in O(k O(1) n log5 n) time.

This work is supported by NSF under grants CNS-05-40347, CFF-06-35000, and DEB-04-25465, by ARO grants W911NF-04-1-0278 and W911NF-07-1-0376, by an NIH grant 1P50-GM-08183-01, by a DOE grant OEGP200A070505, and by a grant from the U.S. Israel Binational Science Foundation.

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Authors and Affiliations

  1. Department of Computer Science, Duke University, Durham, NC 27708

    Pankaj K. Agarwal & Jeff M. Phillips

Authors
  1. Pankaj K. Agarwal
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  2. Jeff M. Phillips
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Dan Halperin Kurt Mehlhorn

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Agarwal, P.K., Phillips, J.M. (2008). An Efficient Algorithm for 2D Euclidean 2-Center with Outliers. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_6

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  • DOI: https://doi.org/10.1007/978-3-540-87744-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87743-1

  • Online ISBN: 978-3-540-87744-8

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